Student handout: Fourier Transform of a Derivative

Periodic Systems

The formula for the inverse Fourier transform shows that a function \(f(x)\) can be written in terms of its Fourier transform via \begin{equation} f(x)= \frac{1}{\sqrt{2\pi}} \int_{-\infty}^{\infty} \tilde{f}(k)\, e^{ikx}\, dk \end{equation} Take the derivative of both sides of this equation with respect to \(x\) and simplify. Interpret your expression as the inverse Fourier transform of something.


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corinne
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Publication Status
Published
Publication Date
Aug. 16, 2023, 2:22 a.m.